The present invention relates to techniques useful for training a multivariable power series. The adaptive systems that are being proposed are the same as that that have been suggested for use with an artificial neural network.
A power series is defined as a weighted sum of product terms. The highest power of a variable in the power series is defined as the order of that variable. As an example:   output  =            ∑              i        ,        j        ,                  k          =          0                            I        ,        J        ,        K              ⁢          xe2x80x83        ⁢                  a        ijk            ⁢              x        1        i            ⁢              x        2        j            ⁢              x        3        k            
The parameter aijk is the weight of the term x1ix2jx3k. In this sum, the highest power of the variable x1 is I. I is said to be the order of the variable x1.
There is a need for an alternative technique for training this system. One technique for adjustment of parameters or training known to the inventor, which may not be prior art to the present invention, is to allocate the level error to the parameters based on their derivatives with output.
In addition, a number of problems must be addressed and overcome before advanced training techniques can be implemented. These include.
1) developing a recursive technique for evaluating a multivariable power series that requires the minimum number of multiplications and additions.
2) permitting the code used in the previous statement to evaluate any power series involving any number of variables and have the power series so developed be of any order with any variable.
3) developing a recursive technique for calculating the derivative of all parameters with the power series"" output, so that these derivatives can be used for training the power series.
4) developing an integrated matrix technique that decides which of two matrix techniques to use or if neither matrix technique can be used because the determinants of the coefficients are zero, providing an alternate technique.
The present invention addresses and overcomes these problems.
According to the invention, a method is provided for using change in input value between two data points to calculate the change output from a multivariable power series as a separate signal. The method of calculating the change output as a separate signal is generalized so that the derivative of all parameters used in the construction of the multivariable power series can be calculated with the change output signal. The availability of this derivative and ability to calculate an error in the level of the change output signal, permits the power series to be trained using the change output signal. The training algorithm according to the invention involves permitting direct calculation of the change output as a separate variable, and also calculation of the derivative of all parameters used in the construction of multivariable power series with this change output. The value of these parameters will be adjusted using the calculated derivatives and the error in the change output signal.
Matrix techniques can be used to increase the training rate. Because no single matrix technique can be used under all circumstances, a further decision technique has been developed for deciding which of three techniques, including two matrix techniques, should be used under a given set of circumstances. When using the technique according to the invention, it is useful to define data-points which combine an array of input values and a desired output value so that it can be adapted to use with new training techniques.
The inventive modification to prior art technology for obtaining a change level output from a power series is use a change variable. This can be done by combining two normal data-points to create a change-data-point. A change-data-point includes an array of change-variable input values and a desired change output value. A change-variable is a structure of level and xcex94level, where xcex94level is the change of level between the two data points. By overloading the multiplication and addition operators a technique has been developed for calculating the change output from the power series directly. By using the same technique, the derivative of all parameters with the change output can be calculated and the power series can be trained using the change-variable.
The existence of efficient techniques for calculating the change output and derivative of all parameters with change output is dependent on the existence of efficient technique for calculating these same items for level training.
The invention will be better understood by reference to the following detailed description in conjunction with the following drawings.